# Book:B. Noble/Numerical Methods 2: Differences, Integration and Differential Equations

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## B. Noble:

## B. Noble: *Numerical Methods 2: Differences, Integration and Differential Equations*

Published $\text {1964}$, **Oliver and Boyd Ltd**.

### Subject Matter

### Contents

- A NOTE FOR THE READER

- VII. FINITE DIFFERENCES AND THE APPROXIMATE REPRESENTATION OF FUNCTIONS
- 7.1 Introduction
- 7.2 Finite difference tables
- 7.3 The use of differences in detecting errors
- 7.4 The differences of a polynomial
- 7.5 The approximate representation of functions
- Examples VII

- VIII. POLYNOMIAL INTERPOLATION
- 8.1 Introduction
- 8.2 Errors in polynomial interpolation
- 8.3 Aitken's method of interpolation by linear crossmeans
- 8.4 Newton's divided-difference interpolation formula
- 8.5 The Gregory-Newton and the Gauss formulae
- 8.6 The Everett, Bessel, and Stirling formulae
- 8.7 Practical interpolation using differences
- Examples VIII

- IX. NUMERICAL INTEGRATION AND DIFFERENTIATION
- 9.1 Introduction
- 9.2 The trapezoidal rule and Simpson's rule
- 9.3 Error estimation: Simpson's rule in hand and automatic computing
- 9.4 The treatment of singularities
- 9.5 Gaussian formulae
- 9.6 Central difference formulae
- 9.7 Numerical differentiation
- Examples IX

- X. ORDINARY DIFFERENTIAL EQUATIONS
- 10.1 Introduction
- 10.2 Elementary considerations
- 10.3 Error estimation when solving differential equations numerically
- 10.4 Programming the numerical solution of differential equations
- 10.5 Runge-Kutta formulae
- 10.6 Predictor-corrector methods
- 10.7 Errors and stability
- 10.8 A comparison of methods
- 10.9 Second-order equations
- 10.10 Two-point boundary conditions
- Examples X

- XI. PARTIAL DIFFERENTIAL EQUATIONS
- 11.1 Introduction
- 11.2 The heat conduction equation
- 11.3 Laplace's equation
- Examples XI

- INDEX